Ever since President Trump landed in the U.K. yesterday, there have been a number of diplomatic ups and downs. One hour, he's criticizing the prime minister directly for how she's handling the U.K.'s imminent departure from the EU. The next, he says Prime Minister May can manage Brexit however she sees fit.

(SOUNDBITE OF PRESS CONFERENCE)

PRESIDENT DONALD TRUMP: I don't know what they're going to do. But whatever you do is OK with me. That's your decision. Whatever you're going to do is OK with us. Just make sure we can trade together. That's all that matters.

MARTIN: But is it? There are protesters lining the streets of London who say otherwise. NPR's London correspondent was out in those demonstrations. He is back in our studios now and joins us. Frank Langfitt, thanks for being here.

FRANK LANGFITT, BYLINE: Hi, Rachel.

MARTIN: So it was a pretty civil press conference, all things considered - I mean, especially in light of the harsh words President Trump had for the prime minister in The Sun newspaper interview. How big of a divide is there right now between the U.S. and the U.K.?

LANGFITT: It would seem pretty big. Despite the civility of the press conference, remember President Trump, overnight basically in this interview that came out in The Sun newspaper tabloid here, said he didn't see a free trade deal between the U.K. and the U.S. anytime soon. And this is very difficult for the United Kingdom. They're leaving the European Union. They're on their own. They're feeling quite lonely. This is their closest ally. And Prime Minister May had really been hoping for much better word. So there's also a real difference, I think, on the trade issue of - Prime Minister May needs to keep some contact with the European Union not to devastate the U.K. economy but not getting the sort of support that she would hope to from Britain's closest friend.

MARTIN: What about President Trump's remarks on immigration? He said that immigration has changed the culture of Europe and not in a good way. The prime minister, then in this press conference, seemed to take issue with that characterization. Let's listen to what she had to say.

(SOUNDBITE OF PRESS CONFERENCE)

PRIME MINISTER THERESA MAY: Over the years, overall immigration has been good for the U.K. It's brought people with different backgrounds, different outlooks here to the U.K. and has - and we've seen them contributing to our society and to our economy.

MARTIN: I mean, this is so awkward. Right? She said that when Trump was standing right next to her.

LANGFITT: Yeah. And - you know, it's interesting. I think that this should get a lot of attention. Even though it's not newsmaking, it's two different visions of an incredibly important issue that is roiling the Western world. We're seeing it in the United States. We see it here in the United Kingdom. We see it across Western Europe. And the kind of approach that Prime Minister May is taking is a much more accepting and open approach. The one that President Trump is taking, which is also shared by a number of leaders in parts of Europe, is - this is a bad thing; it is affecting our way of life; it is affecting the safety of communities in terms of terrorism. So I thought it was really a stark difference in approach that you see in a lot of Europe compared with the leader of the United States.

MARTIN: How popular is Donald Trump's perspective on immigration in the U.K.?

LANGFITT: Not that popular but popular enough to remember that immigration was a driving factor in the Brexit vote two years ago. There will be a small white nationalist protest in favor of Trump and on a number of ethnic issues tomorrow. Trump is not popular here. The recent polls - the YouGov polls that have come out show that the majority of people think he's a misogynist and a sexist. But you know, there are people here who would probably agree with him on the immigration issue. When I was covering the Brexit vote, people talked to me a lot about how they felt their neighborhoods had changed. They didn't feel comfortable in their neighborhoods. And so they would - I think those folks would probably agree with President Trump.

MARTIN: London's mayor, Sadiq Khan, has been a sharp critic of Trump and, in particular, his immigration policies. And in turn, Donald Trump has had very harsh words to say about Khan. But how has Sadiq Khan's approach to Trump differed from May's?

LANGFITT: Absolutely different. And he's in a much (laughter), much better position. He doesn't have a...

MARTIN: Right. Being the mayor of London is a different job.

LANGFITT: Oh, it's so much easier. He doesn't have to worry about the blowback that Prime Minister Theresa May could expect from Donald Trump if she were to publicly challenge him. Sadiq Khan - this, I think, helps him. He's a popular mayor here, son of a Pakistani bus driver, a Muslim. And his approach has been to say what Donald Trump says and does is unacceptable, and it doesn't reflect the values of London. And you know, he's frankly used Donald Trump to really help define himself even further in this city as a defender of these sorts of liberal values and multicultural values which, you know, you and I began the conversation on with immigration.

MARTIN: ...To Helsinki to meet with Vladimir Putin, although other European leaders say that this emboldens an already dangerous regime. What is May's rationale here?

LANGFITT: I think - May didn't go into great detail here. I think that her rationale - to some degree, she seemed to be just supporting the idea that President Trump has said over and over again, which is, it's good to have good relations with important and critical powers, even if you disagree on many issues. And she did offer a little support to him, pointing out that, indeed, President Trump of the United States did expel 60 Russian officials after the poisoning here in the United Kingdom.

MARTIN: All right. NPR London correspondent Frank Langfitt for us this morning covering President Trump's trip to the U.K.